Abstract
In the problem of estimating the covariance matrix of a multivariate normal population, James and Stein (Proc. Fourth Berkeley Symp. Math. Statist. Prob., 1, 361-380, Univ. of California Press) obtained a minimax estimator under a scale invariant loss. In this paper we propose an orthogonally invariant trimmed estimator by solving certain differential inequality involving the eigenvalues of the sample covariance matrix. The estimator obtained, truncates the extreme eigenvalues first and then shrinks the larger and expands the smaller sample eigenvalues. Adaptive version of the trimmed estimator is also discussed. Finally some numerical studies are performed using Monte Carlo simulation method and it is observed that the trimmed estimate shows a substantial improvement over the minimax estimator.
Original language | English |
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Pages (from-to) | 101-108 |
Number of pages | 8 |
Journal | Annals of the Institute of Statistical Mathematics |
Volume | 38 |
Issue number | 1 |
DOIs | |
State | Published - Dec 1986 |
Keywords
- Covariance matrix
- Stein's loss
- Stein's truncation
- Wishart distribution
- adaptive estimator
- minimax estimator
ASJC Scopus subject areas
- Statistics and Probability